Small heavy particles in a fluid flow respond to the flow on a timescale proportional to their inertia or Stokes number St. Their behavior has been thought to be gradually modified as St increases. We show, on the other hand, in the steady spatially periodic laminar Taylor Green vortex flow, that particle dynamics, and their effective diffusivity, actually change in an irregular, nonmonotonic, and sometimes discontinuous manner with increasing St. At St similar to 1, we show chaotic particle motion, contrasting with earlier conclusions for heavy particles in the same flow [Wang et al., Phys. Fluids 4, 1789 (1992)]. Particles may display trapped orbits, or unbounded diffusive or ballistic dispersion, with the vortices behaving like scatterers in a soft Lorentz gas [Klages et al., Phys. Rev. Lett. 122, 064102 (2019)]. The dynamics is nonergodic.